Proceedings of ICFD11:
Eleventh International Conference of Fluid Dynamics
December 19-21, 2013, Alexandria, Egypt
ICFD11-EG-4039
Computational Modelling of H-type Darrius Vertical Axis Wind Turbine with
Multi Element Airfoil Blades
Ahmed M. El Baz1 , Aly R. Refaey2, Mohannad Y. Mohammed2 and Abdallah W. Youssef2
Renewable Energy Systems Simulation Lab
Department of Mechanical Power Engineering
Faculty of Engineering
Ain Shams University, Cairo, Egypt
1 Associate Professor, Corresponding Author, email: Ahmed_elbaz@eng.asu.edu.eg
2 Graduate Students
ABSTRACT
Vertical axis wind turbines (VAWT) have received considerable
attention in the recent years due to their advantages compared
with horizontal axis wind turbines in urban applications. The
Darrius rotor and the H rotor turbine are VAWTs which employ
airfoil shaped blades to extract energy from the wind by virtue
of their high lift capability. More research work is needed to
increase the power coefficient of this type of wind turbines to
match with higher demand for power in small scale
applications. Also, further work is also needed to enable the H
rotor to become self-starting.
The objective of this study is to examine H rotor turbine
performance using multi element airfoil blades. The work
considers effects of adding a trailing edge flap to the airfoil.
Trailing edge flap geometry such as relative length and flap
angle relative to chord length are examined. The present work
shows that this design outperforms that of conventional airfoil
by 15% at low speed ratios. Moreover, the flap angle can
improve the self-starting capability of the turbine by increasing
the lift force on some blades in the stand still condition.
KEYWORDS
Wind turbine, H-shape Darrius, Vertical axis, CFD
INTRODUCTION
With the depletion of fossil fuel energy, alternative energy
sources as well as renewable energy have become the most
popular field of research interest. Wind turbines are considered
one of the most commonly used turbomachine for power
generation nowadays so that it has been increasingly
investigated. From the perspective of urban application, Vertical
Axis Wind Turbine (VAWT) has many advantages over the
widely used conventional Horizontal Axis Wind Turbine
(HAWT). Eriksson et al [1] made a comparative study of three
different wind turbines (HAWT, Darrius VAWT and HVAWT) from the most important aspects including structural
dynamics, control systems, maintenance, manufacturing and
electrical equipment. A case study was presented where the
three different turbines were compared to each other. They
concluded that the vertical axis wind turbine appears to be
advantageous to the horizontal axis wind turbine in several
aspects.
Darrius and H turbine research have examined many
design parameters of these turbines [2-7]. These parameters
include blade profile shape, aspect ratio, solidity, tip speed ratio
as well as others. Some recommendations for the optimum
values of such parameters are now available in the literature.
The majority of VAWTs typically start producing power at wind
speed as low as 3 m/s, which is called the cut in speed. The
rated wind speed may be as high as 11 m/s at some sites
according to the location selected to install the wind turbine.
The maximum wind speed a wind turbine can continue
operation is called the cut out speed which may reach 14 m/s.
Determining the most frequent wind speed at which the wind
turbine will operate is required to predict its performance and
the characteristic dimensions of a wind turbine. Once the
operating wind speed has been chosen, the first step in wind
turbine design is to select the optimum operating tip speed ratio
λ which is defined:
λ = ωR/U∞
(1)
where ω is the rotational speed of the turbine, R is the tip radius
of the turbine and U∞ is the wind speed.
Fig. 1 is a schematic of a straight-three bladed fixed-pitch
H-rotor wind turbine. The geometry of the turbine can be
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defined through the rotor diameter, height and a dimensionless
parameter known as the solidity:
σ = Nc/Drotor
(2)
where N is the number of blades and c is the blade chord
length. The turbine blade is usually constructed of symmetric
airfoils (e.g. NACA 00xx). The performance of the turbine is
dependent on the selected airfoil section. NACA 0015, 0018
sections have been used in several designs [2].
The turbine motion depends mainly on the
aerodynamic forces on the airfoil section, Fig.2 [3]. Wind
velocity is blowing on the airfoil at an angle of attack α. The
lift and drag forces on the airfoil are shown normal and parallel
to the wind direction. Both forces can be resolved in the
direction of blade motion to calculate the thrust force (T) and
the normal force (N). The thrust and normal force coefficients
are related to the lift and drag coefficients and the angle of
attack as follows:
CT = CL sin (α) – CD cos (α)
CN = CL cos (α) – CD sin (α)
(3)
(4)
Where (CT) is the thrust force coefficient driving the
turbine, and (CN) is the normal force coefficient.
The variation of the angle of attack according to the
azimuth position of the blade is given by the following relation,
Fig.3.
α = tan-1[(sin θ)/(λ+cos θ)]
where θ is the azimuthal angle and λ is the tip speed ratio. As
can be seen in Fig. 3, for high speed ratio (λ>3) the angle of
attack is less than 15o. Such angle is close to stall angle of
symmetric airfoils. For lower speed ratios, the angle of attack
may exceed the stall angle and the turbine blade thrust force
diminishes during most of the cycle of rotation. Thus, a turbine
blade would develop useful thrust during a quarter of the cycle
only (~90o).
Fig.1: Three bladed H-rotor Darrieus turbine [9].
Fig.3: Angle of attack variation with azimuth position.
For a Darrieus rotor diameter (D), height (H) and free
stream velocity (U∞), the mechanical torque coefficient Cm and
the power coefficient Cp can be written:
Cm = [2T/ρARU2 ]
(5)
And,
Cp = [2P/ρAU3 ]
(6)
where (T) and (P) are the torque and the power developed,
respectively, and (A) is the swept area of the rotor.
A = Drotor Hrotor
(7)
Fig.2: Force coefficients of a blade element airfoil [3].
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Typical values of the power coefficient of Darrius turbine can
reach 35% at a tip speed ratio between 5 and 6 (Sandia
SAND0015/47 – NACA 0015 airfoil sections) [1].
Several investigations have been reported in the
literature to improve the performance of the H- rotor turbine
using CFD. These investigations have shown the validity of
numerical techniques to reproduce qualitative and quantitative
agreement with the experimental data available for Darrius
turbines. Castelli et al [4] presented a numerical model
for the evaluation of energy performance and aerodynamic
forces acting on a straight bladed vertical-axis Darrius wind
turbine using 2-D simulations of a classical NACA 0021 threebladed rotor. The obtained results have shown the reduction of
blade relative angles of attack passing from lower to higher
TSR values, due to the increasing influence of blade
translational speed in the near-blade flow field. The azimuthal
positions of maximum power extraction along blade trajectory
have been located inside the 4th and 5th octants, probably due
to the combination of a great energy extraction exerted by the
rotor blade (due to the upwind operation of the rotor blade
itself) and a relative high lever arm with respect to the rotor
axis.
Vassberg et al. [5] reported efficiency improvement of a
vertical-axis wind turbine through the application of the CFD
capabilities through the simulation of the dynamic motion of a
turbine blade spinning about a vertical axis and subjected to a
far-field uniform free-stream velocity flow field. Roynarin et al.
[6] have studied power curves for a prototype of an H-rotor and
their test results showed improved performance. Their
theoretical results predict a maximum CP of 0.54 at a tip
speed ratio of 2.5 for a small H-rotor. The investigation made
by Argren et al. [7] also show very promising results for the
performance of the H-rotor. Their high theoretical CP makes the
authors question if the Betz limit is the upper limit of the power
coefficient for VAWTs. Mertens et al. [8] have showed that
the power coefficient of an H-rotor is higher than the power
coefficient of a HAWT when the turbine is placed on a rooftop.
Experimental results from different studies on straight bladed
H-rotors from the literature were summarized in [1] too. The
maximum Cp was 0.43 at a tip speed ratio of 3.
The objective of the present work is to apply the CFD
technique to investigate the performance of the H rotor turbine.
Further, a modified airfoil section is proposed to improve the
performance at low tip speed ratios. The Model is validated by
reference to experimental measurements reported in the
literature.
GOVERNING
EQUATIONS
AND
NUMERICAL
SOLUTION SCHEME
In the present work the unsteady Reynolds averaged Navier
Stokes equations are solved. For incompressible flow, these
equations are written in tensorial form:
Continuity Equation
∂u i ∂u i
+
=0
∂t ∂xi
(8)
Momentum Equation
∂u i
∂u
∂
1 ∂P
+uj i = −
−
∂t
∂x j
ρ ∂xi ∂x j
⎡ ⎛ ∂u i ∂u j 2 ∂u l ⎞⎤ ∂
⎟⎥ +
+
− δ ij
− ui′u ′j
⎢ν ⎜⎜
⎢⎣ ⎝ ∂x j ∂xi 3 ∂xl ⎟⎠⎥⎦ ∂x j
(
(9)
Equations 8 and 9 include three unknowns; the mean
velocity ui , mean pressure P and the Reynolds stresses − ui′u ′j .
To solve these equations a model for the Reynolds stresses
should be prescribed. In the present work the Bousinesq
approximation of the Reynolds stresses is adopted, which is
written [12]
⎛ ∂u
∂u j
− u i′u ′j = ν t ⎜ i +
⎜ ∂x
⎝ j ∂xi
where
ν t is
⎞ 2⎛
⎟ − ⎜ k + ν t ∂u m
⎟ 3⎜
∂x m
⎝
⎠
⎞
⎟⎟δ ij
⎠
(7)
the kinematic eddy viscosity, k is the turbulent
kinetic energy and
δ ij is the unit tensor. The model is
completed by obtaining the kinematic eddy viscosity.
Spalart-Allmaras (S-A) model [11] has been chosen for the
turbine simulation using the vorticity-strain based production.
This modification to the model has been proposed [12] to take
into account the effect of mean strain on the turbulence
production. including both the rotation and strain tensor more
correctly. Therefore, the model accounts for the effects of
rotation on turbulence as it reduces the production of eddy
viscosity and consequently reduces the eddy viscosity itself in
regions where the measure of vorticity exceeds that of strain
rate. Spalart-Allmaras model has been shown to give good
results for boundary layers subjected to adverse pressure
gradients. It is also gaining popularity in the turbomachinery
application [13]. The model also has several favorable
numerical features, as it requires only moderate grid resolution
in the near-wall region and has the capability of fast converging
comparing with the two-equation models.
CFD MODEL VALIDATION
A 2D computational model was constructed for an H-rotor
Darrius turbine. Table 1 represents the main geometrical
features of the tested model which has been chosen identical to
the experimental model presented in [4].
Table.1: Turbine main geometrical features.
Drotor[m]
Hrotor[m]
N[-]
Blade profile
C [mm]
σ[-]
3
1.03
1
3
NACA 0021
85.8
0.25
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)
Choosing a suitable computational domain is a key step in
correctly reproducing fluid-dynamic phenomena. Firstly, the
computational domain has to be suitable for reproducing the
wind turbine rotation allowing a full development of the wake.
The domain also has to be optimized, since using too large
domain would lead to unnecessary increase in the number of
cells and hence the computational time. A circular domain was
selected to enable good quality meshing. The domain diameter
was selected to be 20 times the turbine rotor diameter [9]. A
multi zone domain was constructed as shown in Fig. 4. The
rotating zone, which encloses the rotor blades, has an inner
diameter of 0.75 Drotor and an outer diameter of 1.25 Drotor. The
dimensions of the different zones are shown in table 2.
Table.2: Main computational domain dimensions.
Outer domain
20 Drotor
Rotor sub-domain
2 Drotor
Ring outer diameter
1.25Drotor
Ring inner diameter
0.75Drotor
Fig. 5 Rotating zone (in yellow color)
Spatial discretization of the flow domain was the result of
a series of grid independency tests. The grid size was gradually
refined until the difference between the numerical results of the
same simulation was negligible resulting of different mesh size
ranging from 150,000 up to 500,000 cells. An unstructured grid
was generated for the rotor sub-domain and the rotating ring.
Following the work of T.J. Baker [10], the hybrid grid was
chosen for the airfoil surface to be able to fully resolve the
viscous sub-layer with high accuracy. The first cell height was
set to be 0.005 mm, to keep the value of y+<1for all azimuthal
positions of the blades. The used mesh in this work is shown in
Fig. 6.
Fig. 4 The solution domain
Fig. 5 shows an enlarged view of the rotating zone which
includes the rotor blades. The blades rotate in the counter clock
wise direction. The rotating zone has two sliding mesh surfaces
which are connecting this zone to the inner and outer flow
zones.
Fig.6: The hybrid grid near airfoil leading edge.
The unsteady Reynolds Averaged Navier Stokes euations
were solved by the ANSYS Fluent 14 solver using the Sliding
Mesh Model (SMM) to consider the physics of rotor rotation
effects. Following Castelli et al. [4], the unsteady performance
of the turbine rotor was simulated with a constant inlet velocity
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of 9 m/s, while changing the rotor rotational speed to obtain
different tip speed ratios. The time step size has been set for
each rotational speed corresponding to a rotation angle of 1◦.
The SIMPLE algorithm for pressure-velocity coupling,
whereas the discretization has been performed using the finitevolume method with third-order (MUSCL) scheme for flow
variables and second-order implicit for time discretization. In
the iterative process of equation solving, the solution was
considered to be converged when the continuity residual was
less than 10-5 for each time step. Residuals of other flow
variables were less than 10-8.
The calculations were carried on until reaching the cyclic
behavior of the power coefficient where the last two cycles
have the same average torque coefficient with a deviation of
less than 1%. The average Cm presented in this work was the
average of last two cycles for the each simulation. Each case
may require from 6 up to 17 cycles to reach the quasi-steady
solution. Fig. 7 presents how the computed average torque
coefficient approaches the quasi-steady state for the validation
case at λ = 3.3.
Fig. 8 shows a comparison between the predicted and
measured values of the turbine rotor power coefficient variation
with tip speed ratio for the selected three bladed rotor [4]. The
figure shows that the model results are in very good agreement
with the measurements reported in [4]. The power coefficient
was obtained by averaging the power developed over two
complete cycles. The results show that the power coefficient
has a maximum value 0f 0.32 near a tip speed ratio of 2.65.
Cm avg.
.
Cycles
Fig. 7 Variation of average moment coefficient with number of
cycles (λ=3.3).
Fig. 8 Comparison between computed (present) and
experimental [4] variation of power coefficient with tip speed
ratio for 3 bladed rotor.
MULTI ELEMENT AIRFOIL GEOMETRY
The concept of multi element airfoil geometry was
developed in the aeronautical industry in order to increase the
lift capacity of blasé sections used for aircraft wings by adding
leading edge slats and trailing edge flaps. The former
modification aims at generating a wall jet at the leading edge of
the airfoil which can delay boundary layer separation at high
angle of attack. The trailing edge flap also aims at increasing
lift force by extending the airfoil downstream and increasing its
effective camber. In the present work leading edge slat was
found to have adverse effect on the turbine performance due to
the increased drag which is effective over three quarters of the
blade cycle. Addition of trailing edge flap was found to
improve the power coefficient at low speed ratios. Therefore,
the results of simulations using trailing edge flap only will be
presented.
Using NACA 0021 section the trailing edge flap was added
with the dimensions proposed by Lowry and McKay [14]. The
geometry of the flap is shown in Fig. 9 and table 4. Three
angles of the flap were tested in order to obtain maximum
power coefficient for the turbine rotor at speed ratio of 2.65.
Figure 10 shows the computed results for the three angles of
10, 20 and 30 degrees compared with the results of airfoil
without flap. Slight improvement of the power coefficient was
found with flap angle of 10 degrees. Therefore, results for this
flap shall be presented for other tip speed ratios. Fig. 11 shows
the airfoil geometry with the mesh used with the flap.
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Fig.9 Modified airfoil and flap dimensions [11].
Table.4: Modified airfoil and flap dimensions [11].
Flap section
NACA 0021
X
3.83% C
Y
3.45% C
Cf (Flap chord length)
0.2566 C
Fig.10 Optimization of flap angle of inclination (λ=2.65).
Fig. 11 Airfoil geometry and mesh with trailing edge flap
RESULTS AND DISCUSSION
Figure 12(a-c) shows the predicted variation of the
instantaneous torque coefficient during one cycle for tip speed
ratios 2.0, 2.33 and 2.5, respectively, for the three bladed rotor
with and without blade flaps. In each figure three peaks of the
torque coefficient are observed, each one corresponds to one
blade of the three bladed rotor. Although introducing the
trailing edge flap was not able to increase the maximum
instantaneous Cm, it leads to diminishing the negative values
for the shown tip speed ratios. The trailing edge flap effect is
more pronounced for the lower speed ratio, Fig. 12 a. However,
for high speed ratio the torque coefficient is very close to that
predicted without flap.
The increased torque coefficient at low tip speed ratio
could decrease the problem of Darrieus turbine self-starting
discussed in [15]. The presence of the flap increases the airfoil
lift at high angles of attack encountered at low rotational speed
of the turbine when the main turbine airfoil blade has a high
incidence angle with the relative wind velocity vector.
Figure 13 shows the predicted variation of the average
power coefficient of the turbine rotor with tip speed ratio, with
and without blade flaps. As can be seen in the figure, at low
speed ratios the turbine rotor with trailing edge flap results in
increasing the power extracted by turbine rotor blades due
cancelling the negative torque on the rotor blades at low speed
ratios. The peak power coefficient is close to that predicted
without flap and occurs at close value of the tip speed ratio.
Figure 14 and 15show the predicted streamlines around the
three blades of the turbines which are positioned 120 degrees
apart. Blades 1, 2 and 3 are located at 0, 120 and 240 degrees.
This orientation of the rotor blades corresponds to the
minimum value of the torque coefficient of the turbine rotor as
shown on Fig. 13. The streamlines around blade 1 are almost
identical for the original blade and the blade with trailing edge
flap. For blade 2, however, the presence of the flap causes reattachment over the back side of the blade which reduces the
drag on the blade and cancels the negative torque on the blade.
Similar effect is shown on blade 3 too. The reattachment on the
trailing edge flap results due to the leak flow through the gap
between the main airfoil section and the trailing edge flap.
CONCLUSION
In this paper, unsteady RANS equations were solved with
the Spalart-Allmaras turbulence model to simulate the flow
around the H-shaped three bladed VAWT rotor using a 2D
modeling approach. The model results in accurate values of the
power coefficient of the three bladed turbine using NACA 0021
airfoil section compared to the experimental results. The
simulations were extended to examine the effect of introducing
trailing edge flap to the airfoil on the turbine rotor performance
compared with the original blade design without trailing edge
flap. The results showed that the modified design results in
high values of the power coefficient at low speed ratios. This
effect is attributed to the cancelation of the negative torque on
the turbine rotor observed at some azimuthal angles of the
turbine rotor. This effect was attributed to the reattachment of
the flow on the trailing edge flap at the positions of high angle
of attack which corresponds to negative thrust force on the
turbine blades. This effect can also improve the self-starting
capability of the turbine.
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Fig.12.a Instantaneous moment coefficient variation with
azimuthal angle (λ=2.0)
Fig.13 Comparison of the Cp variation with tip speed ratio, with
and without the flap (10 degree flap)
Fig.12.b Instantaneous moment coefficient variation with
azimuthal angle (λ=2.33)
Fig.12.c Instantaneous moment coefficient variation with
azimuthal angle (λ=2.5)
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WITHOUT TRAILING EDGE FLAP
WITH TRAILING EDGE FLAP
Blade 1 at 0 degree
Blade 1 at 0 degree
Blade 2 at 120 degree
Blade 2 at 120 degree
Blade 3 at 240 degree
Fig. 14 Streamlines around turbine rotor blades at minimum
torque with flap
Blade 3 at 240 degree
Fig. 15 Streamlines around turbine rotor blades at minimum
torque without flap
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NOMENCLATURE
A [m2] rotor swept area
c [mm] blade chord
CF [mm] flap chord length
CD [-] drag coefficient
CL [-] lift coefficient
CT [-] thrust force coefficient
CN [-] normal force coefficient
CP [-] rotor average power coefficient
Cm [-] rotor instantaneous torque coefficient
Drotor [m] rotor diameter
Hrotor [m] rotor height
N [-] number of rotor blades
R [m] rotor radius
U [m/s] absolute wind velocity
α [o] blade relative angle of attack
θ [o] blade azimuth position
ρ [kg/m3] air density
σ [-] rotor solidity
ω [rad/s] rotor angular velocity
λ [-] tip speed ratio
ABBREVIATIONS
CFD
Computational Fluid Dynamics
HAWT
Horizontal Axis Wind Turbine
MUSCL
Monotone Upstream-centered Schemes for
Conservation Laws
SIMPLE
Semi-Implicit Method for Pressure Linked
Equations
SMM
Sliding Mesh Model
VAWT
Vertical Axis Wind Turbine
Proceedings from IMAREST conference MAREC 2002,
Newcastle, UK.
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Wind Eng 2003;27(6):507–18.
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documentations, 2009
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Maxwell slat and with trailing-edge flaps”, Langley
Memorial Aeronautical Laboratory, Langley field, VA,
1941.
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“Self-starting capability of a Darrieus turbine”,
Proceedings of the Institution of Mechanical Engineers,
Part A: Journal of Power and Energy vol. 221 no.1 (111120), UK, 2007.
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